POJ1579

http://poj.org/problem?id=1579
Function Run Fun
Time Limit: 1000MS  Memory Limit: 10000K
Total Submissions: 11121  Accepted: 5815

Description

We all love recursion! Don't we?

Consider a three-parameter recursive function w(a, b, c):

if a <= 0 or b <= 0 or c <= 0, then w(a, b, c) returns:
1

if a > 20 or b > 20 or c > 20, then w(a, b, c) returns:
w(20, 20, 20)

if a < b and b < c, then w(a, b, c) returns:
w(a, b, c-1) + w(a, b-1, c-1) - w(a, b-1, c)

otherwise it returns:
w(a-1, b, c) + w(a-1, b-1, c) + w(a-1, b, c-1) - w(a-1, b-1, c-1)

This is an easy function to implement. The problem is, if implemented directly, for moderate values of a, b and c (for example, a = 15, b = 15, c = 15), the program takes hours to run because of the massive recursion.

Input

The input for your program will be a series of integer triples, one per line, until the end-of-file flag of -1 -1 -1. Using the above technique, you are to calculate w(a, b, c) efficiently and print the result.
Output

Print the value for w(a,b,c) for each triple.
Sample Input

1 1 1
2 2 2
10 4 6
50 50 50
-1 7 18
-1 -1 -1
Sample Output

w(1, 1, 1) = 2
w(2, 2, 2) = 4
w(10, 4, 6) = 523
w(50, 50, 50) = 1048576
w(-1, 7, 18) = 1

从题意很容易写出代码,但是超时,想了想，用记忆性搜索可以很好的解决此题

#include <stdio.h>
#include <math.h>
#include <string.h>

int dp[21][21][21];

int w(int a, int b, int c)
{
	if(a <= 0 || b <= 0 || c <= 0)
	{
		return 1;
	}else if(a > 20 || b > 20 || c > 20)
	{
		return 1048576;
	}else if(a <= b && b <= c)
	{
		if(dp[a][b][c] == -1)
			dp[a][b][c] = (int)pow(2, a);
		return dp[a][b][c];
	}else
	{
		if(a-1 >= 0&&dp[a-1][b][c] == -1)
			dp[a - 1][b][c] = w(a-1, b, c);
		if(a - 1 >= 0 && b - 1 >= 0 &&dp[a-1][b - 1][c] == -1)
			dp[a- 1][b - 1][c] = w(a-1, b- 1, c);
		if(a- 1 >= 0 && c - 1 >= 0 && dp[a - 1][b][c - 1] == -1)
			dp[a- 1][b][c - 1] = w(a - 1, b, c - 1);
		if(a - 1 >= 0 && b - 1 >= 0 && c - 1 >= 0)
			dp[a- 1][b - 1][c - 1] = w(a - 1, b - 1, c - 1);
     	return dp[a - 1][b][c] + dp[a- 1][b - 1][c] + dp[a- 1][b][c - 1] - dp[a- 1][b - 1][c - 1];
	}
}

//此题有如下规则:
//1.当a b c中有任意一个数大于20 则返回1048576
//2.如果 a<=b<=c 则返回 pow(2, a)
//3.其他的数据可以用记忆性搜索来提高时间
int main()
{
	int a, b, c;
	memset(dp, -1, sizeof(dp));
	while(scanf("%d%d%d", &a, &b, &c) == 3)
	{
		if(a == -1 && b == -1&& c== -1)
			break;
		printf("w(%d, %d, %d) = %d\n", a, b, c, w(a, b, c));
	}
	return 0;
}